A conventional control system, as described in U.S. Pat. No. 5,451,849, for controlling a motor-vehicle convertible-top system has a plurality of components movable by electromotive drives. Belonging to the components is a convertible top having a plurality of bows that are movable between a fully extended state in which the convertible top covers the motor vehicle, and a completely retracted state, as well as a cover for a convertible-top housing in which the convertible top is accommodated in the open state.